The present invention relates to a method of and an apparatus for training tap coefficients of an adaptive equalizer, and particularly to the method of and the apparatus for optimizing tap coefficients of a FIR (Finite Impulse Response) filter used as an adaptive equalizer to equalize a multicarrier data signal that has been transmitted through a distorting channel.
In a multicarrier data transmission system, input digital data are grouped into blocks, called symbols, of a certain number of parallel bits. The parallel bits of a symbol are further divided into a plurality of bit sets, and each of the bit sets is used to modulate each one of the same number of carrier signals of different frequencies. A preferred method of modulation/demodulation is a modulation to use an IFFT (Inverse Fast Fourier Transformation) and a demodulation to use a FFT (Fast Fourier Transformation).
FIG. 12 is a block diagram illustrating a system configuration of the multicarrier data transmission system, having a transmitter 300 comprising an encoder 120, an IFFT circuit 130 and a D/A (Digital to Analog) converter 140, and a receiver 400 for receiving a multicarrier data signal transmitted from the transmitter 300 through a transmission channel 200, comprising an A/D (Analog to Digital) converter 410, a FFT circuit 430, a FEQ (Frequency-domain EQualization) circuit 440 and a decoder 450. As to an adaptive equalizer 420 and a training circuit 500, they will be described afterwards.
When a symbol consists of binary data of 512 bits for modulating 256 carrier signals, for example, the encoder 120 divides the binary data into 256 sets of 2 bits, and encodes each n-th (n=1 to 256) component of a 256- dimensional frequency-domain vector representing the 256 carrier signals by n-th of the 256 sets of 2 bits, as follows. When the logic of n-th 2-bit set is {0, 0}, {0, 1}, {1, 0} or {1, 1}, the n-th component of the frequency-domain vector is encoded as 1+j, 1-j, -1+j or -1-j, for example, j being an imaginary.
The frequency-domain vector thus encoded is transformed into a time-domain digital signal by the IFFT circuit 130 and converted by the D/A converter 140 into an analog signal to be transmitted through the transmission channel 200 as the multicarrier data signal.
The multicarrier data signal received by the receiver 400 is sampled and converted into a time-domain digital signal by the A/D converter 410 and further transformed into a frequency-domain vector by the FFT circuit 430. The FEQ circuit 440 performs frequency-domain equalization of the frequency-domain vector for compensating distortion of the frequency-domain vector due to attenuation and delay caused through the transmission channel 200, and the decoder 450 reproduces the symbol data by decoding each component of the frequency-domain vector.
However, when duration of the impulse response of the transmission channel 200 is not negligible compared to symbol length, inter-symbol interference, that is, interference of a symbol with a preceding or a following symbol, or inter-channel interference, that is, interference of a signal of a carrier frequency with signals of neighboring carrier frequencies due to transmission distortion becomes dominant and impossible to be compensated by the above frequency-domain equalization.
A method developed for dealing with this problem is to shorten duration of the impulse response by compensating and equalizing the time-domain digital signal samples by the A/D converter 410, by performing convolution of the time-domain digital signal through a FIR filter 420 provided between the A/D converter 410 and the FFT circuit 430, and the training circuit 500 for optimizing tap coefficients of the FIR filter 420 so as to correctly equalize the transmission characteristic of the transmission channel 200.
A usual method of optimizing the tap coefficients of the FIR filter 420 is to repeatedly generate and transmit a PRBS (Pseudo-Random Binary Sequence) from the transmitter 300, and to make each of the tap coefficients converge into an optimum value at the receiver 400 by comparing the signal received from the transmitter 300 with a corresponding signal obtained from the same PRBS generated at the receiver side. The FIR filter 420 which has variable tap coefficients to be optimized for equalizing duration of the impulse response is hereinafter called the adaptive equalizer, and a process of and a means for optimizing the tap coefficients are called the training and the training circuit.
The present invention pertains to the training method and the training circuit for stably and rapidly optimizing tap coefficients of the adaptive equalizer.
As a prior art of the training method, there is a technique disclosed in a U.S. Pat. No. 5,285,474.
FIG. 13 is a block diagram illustrating a training circuit according to the prior art. The training circuit of FIG. 13 consists of a transmitter 100 and a receiver 1000 and performs training of tap coefficients of an adaptive equalizer (not depicted in FIG. 13) provided in the receiver 1000 for equalizing signal distortion due to transmission characteristic of a transmission channel 200 connecting the transmitter 200 and the receiver 1000.
The transmitter 100 comprises a first PRBS generator 110 for generating a PRBS signal, a first encoder 120 for encoding the PRBS signal into a frequency-domain transmission signal vector X, an IFFT circuit 130 for transforming the frequency-domain transmission signal vector X into a time-domain transmission signal x(D). (Hereinafter, a frequency-domain vector is denoted by a capital letter and a time-domain signal obtained by processing the frequency-domain vector with IFFT is expressed as a function of discrete delay variable D denoted by a corresponding small letter.)
The time-domain transmission signal x(D) is converted into analog signal, transmitted through the transmission channel 200, received by the receiver 1000 and converted again into a time-domain reception signal y(D). (Ordinary elements such as D/A and A/D converters are omitted to depict in FIG. 13.)
Here, following equation stands; EQU y(D)=x(D)*h(D)+n(D)
wherein h(D) and n(D) represent the impulse response and the noise signal of the transmission channel 200, and the operator `*` denotes convolution operation.
The above equation is expressed as Y=XH+N in the frequency domain.
The receiver 1000 comprises a second PRBS generator 1200 for generating a replica of the PRBS signal generated by the first PRBS generator 110, a second encoder 1250 for generating a frequency-domain training vector X' by encoding a frequency domain vector with the replica of the PRBS signal in the same way and in synchronization with the first encoder 120, a target-impulse-response update means 1300, a target-impulse-response windowing means 1400, a tap-coefficient update means 1500 and a tap-coefficient windowing means 1600.
The target-impulse-response update means 1300, the target-impulse-response windowing means 1400, and tap-coefficient update means 1500 and the tap-coefficient windowing means 1600 operate so as to make tap coefficients of the adaptive equalizer having L taps (L being a fixed integer) converge into optimum values which enable the adaptive equalizer to equalize and shorten the duration of the impulse response H, or h(D), of the transmission channel within v taps (v being another fixed integer), that is, within target duration of the equalized impulse response, by updating transitional values of the target impulse response and the tap coefficients alternately and repeatedly, referring to the reception signal y(D) and the training vector X'.
In the following paragraphs, outlines of operation of the target-impulse-response update means 1300, the target-impulse-response windowing means 1400, the tap-coefficient update means 1500 and the tap-coefficient windowing means 1600 will be described in the order.
The target-impulse-response update means 1300 outputs an updated target impulse response B.sub.u by updating a windowed target impulse response B.sub.w outputted from the target-impulse-response windowing means 1400 (as will be described afterwards), making use of the reception signal y(D), the training vector X' and windowed tap coefficients w.sub.w (D) outputted from the tap-coefficient windowing means 1600 (as will be described also afterwards), so that the updated target impulse response B.sub.u better approximates the frequency-domain vector HW of the equalized impulse response h(D) * w.sub.w (D) of the transmission channel 200. (Hereinafter, the subscript "u" refers to an updated quantity and the subscript "w" refers to a windowed quantity.)
In other words, the target-impulse-response update means 1300 asymptotically and recursively revises the windowed target impulse response B.sub.w towards a target, that is, a frequency-domain vector of an impulse response whereof duration can be equalized within v taps by the adaptive equalizer.
First, initial values of the windowed target impulse response B.sub.w and the tap coefficients w.sub.w (D) are set reasonably, then a loop of steps is repeated until a predetermined convergence condition is reached.
The windowed target impulse response B.sub.w is updated making use of either a frequency-domain LMS (Last Mean Square) method or a frequency-domain division method.
When the frequency-domain LMS method is employed, an error value E is calculated according to following equation (1) as a difference between the windowed target impulse response B.sub.w multiplied by the training vector X', which corresponds to a target reception signal, and the frequency-domain reception signal vector Y multiplied by a frequency-domain vector W.sub.w of the windowed tap coefficients w.sub.w (D), which corresponds to the equalized reception signal. EQU E=B.sub.w X'-W.sub.w Y (1)
Then, the updated target impulse response B.sub.u is obtained according to following equation (2) from the error value E. EQU B.sub.u =B.sub.w +2 .mu.EX* (2)
where .mu. is the LMS stepsize and X* denotes the complex conjugate of the training vector X'.
When the frequency-domain division method is employed, the updated target impulse response B.sub.u is calculated from above equation (1) as the windowed impulse response B.sub.w which gives the error value E=0, as follows; EQU B.sub.u =W.sub.w Y/X' (3)
The target-impulse-response windowing means 1400 windows the updated target impulse response B.sub.u into the windowed target impulse response B.sub.w having v taps in the time-domain, as follows.
The updated target impulse response B.sub.u is transformed into a time-domain signal b.sub.u (D) through the IFFT, whereof consecutive v taps (or samples), which give a maximum total power, are selected, zeroing other taps. The selected consecutive v taps are then normalized to have a fixed power for preventing the training from converging into the all-zero, that is, B.sub.w =w.sub.w (D)=0. The normalized time-domain signal b.sub.w (D) of v taps is transformed again into a frequency-domain vector through the FFT and outputted as the windowed target impulse response B.sub.w, to be updated at the next step by the target-impulse-response update means 1300.
The tap-coefficient update means 1500 updates the windowed tap coefficients w.sub.w (D), in a similar way with the target-impulse-response update means 1300, that is, produces an updated tap-coefficient vector W.sub.u by updating the windowed tap coefficients w.sub.w (D) outputted from the tap-coefficient windowing means 1600 after windowed into L taps, referring to the windowed target impulse response B.sub.w outputted from the target-impulse-response windowing means 1400, the time-domain reception signal y(D) and the training vector X', so as to reduce the error value E given by above equation (1), making use of the frequency-domain LMS method or the frequency-domain division method.
The updated tap-coefficient vector W.sub.u is calculated according to following equation (4) when the frequency-domain LMS method is applied, or according to equation (5) when the frequency-domain division method is applied. EQU W.sub.u =W.sub.w +2 .mu.EY* (4) EQU W.sub.u =B.sub.w Y/X' (5)
where .mu. is the LMS stepsize, W.sub.w is the frequency-domain vector of the windowed tap coefficients w.sub.w (D), and X* denotes the complex conjugate of the training vector X'.
The tap-coefficient windowing means 1600 windows the updated tap-coefficient vector W.sub.u with a time-window of L taps in a similar way with the target-impulse-response windowing means 1400, as follows.
The updated tap-coefficient vector W.sub.u is expanded in the time-domain as the updated tap coefficients w.sub.u (D) through the IFFT, whereof consecutive L taps (coefficients) which give a maximum total power are selected, zeroing other taps. The selected consecutive L tap coefficients are outputted as a first to an L-th component of the windowed tap coefficients w.sub.w (D), which are to be referred to by the target-impulse-response update means 1300 and to be updated by the tap-coefficient update means 1500 at the next step of the convergence loop.
In the prior art of FIG. 13, by generating The PRBS signal repeatedly in synchronization with each other at the transmitter 100 and the receiver 1000, the training steps at the target-impulse-response update means 1300, the target-impulse-response windowing means 1400, the tap-coefficient update means 1500 and the tap-coefficient windowing means 1600 are repeated until a predetermined convergence condition is reached, that is, until the error value E of equation (1) becomes within a threshold value, for example, and by applying convergence values of the windowed tap coefficients w.sub.w (D) thus obtained to the tap coefficients of the adaptive equalizer, the inter-symbol interference and the inter-channel interference are eliminated from the reception signal transmitted through the severe transmission cannel, impulse response duration of the transmission channel being equalized and sufficiently shortened by the adaptive equalizer.
In the above prior art, either or both of the windowed target impulse response B.sub.w and the windowed tap coefficients w.sub.w (D) may be updated either one of the frequency-domain LMS method and the frequency-domain division method. Therefore, following four applications can be considered:
1. To update both the windowed target impulse response B.sub.w and the windowed tap coefficients w.sub.w (D) making use of the frequency-domain LMS method; PA1 2. To update the windowed target impulse response B.sub.w making use of the frequency-domain LMS method, and the windowed tap coefficients w.sub.w (D) making use of the frequency-domain division method; PA1 3. To update the windowed target impulse response b.sub.w making use of the frequency-domain division method, and the windowed tap coefficients w.sub.w (D) making use of the frequency-domain LMS method; and PA1 4. To update both the windowed target impulse response B.sub.w and the windowed tap coefficients w.sub.w (D) making use of the frequency-domain division method. PA1 a transmission step of transmitting a transmission signal x(D) which is produced by transforming a frequency-domain transmission vector X encoded with a PRBS (Pseudo-Random Binary Sequence) into a time-domain; PA1 a target-impulse response update step of producing an updated target impulse response B.sub.u by dividing an equalized reception signal vector Z with a training vector X', the equalized reception signal vector Z being produced by transforming an equalized reception signal z(D), which is obtained by processing the transmission signal y(D) received through the transmission channel with an equalizer having the first number of taps whereof coefficients are set to have values of the windowed tap coefficients w.sub.w (D), into a frequency-domain, and the training vector X being produced by encoding a frequency-domain vector with a replica of the PRBS; PA1 a target-impulse-response windowing step of outputting a windowed target impulse response B.sub.w together with a normalization coefficient S, the windowed target impulse response B.sub.w being produced by transforming the updated target impulse response B.sub.u into a time-domain updated target impulse response signal b.sub.u (D), selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response b.sub.u (D), normalizing the selected consecutive tap values and transforming the normalized consecutive tap values into the frequency-domain, and the normalization coefficient S being obtained by dividing the normalized consecutive tap values with the selected consecutive tap values before normalization; PA1 a tap-coefficient update step of producing an updated tap coefficient vector W.sub.u by updating a frequency-domain tap coefficient vector W.sub.w multiplied by the normalization coefficient S making use of a frequency-domain LMS (Least Mean Square) method with an error value E' defined as a difference of a product of the training vector X' and the windowed target impulse response B.sub.w to a product of the normalization coefficient S, the frequency-domain tap coefficient vector W.sub.w and a reception signal vector Y, the frequency-domain tap coefficient vector W.sub.w being obtained by transforming the windowed tap coefficients w.sub.w (D) into the frequency-domain, and the reception signal vector Y being obtained by transforming the transmission signal y(D) received through the transmission channel into the frequency-domain; and PA1 a tap-coefficient windowing step of producing the windowed tap coefficients w.sub.w (D) by transforming the updated tap coefficient vector W.sub.u into updated tap coefficients w.sub.u (D), selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients w.sub.u (D) and shifting the selected consecutive coefficients to be assigned from a top of the windowed tap coefficients w.sub.w (D). PA1 a target-impulse-response windowing step of producing the windowed target impulse response B.sub.w by transforming the updated target impulse response B.sub.u into the time-domain updated target impulse response signal b.sub.u (D), selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response b.sub.u (D) and transforming the selected consecutive tap values into the frequency-domain; PA1 a tap-coefficient update step of producing the updated tap coefficient vector W.sub.u by updating the frequency-domain tap coefficient vector W.sub.w making use of the frequency-domain LMS method with an error value E defined as a difference of a product of the training vector X' and the windowed target impulse response B.sub.w to a product of the frequency-domain tap coefficient vector W.sub.w and the reception signal vector Y; and PA1 a tap-coefficient windowing step of producing the windowed tap coefficients w.sub.w (D) by transforming the updated tap coefficient vector W.sub.u into updated tap coefficients w.sub.u (D), selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients w.sub.u (D), normalizing the selected consecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients w.sub.w (D). PA1 a target-impulse-response update step of producing the updated target impulse response B.sub.u by updating the windowed target impulse response B.sub.w multiplied by a normalization coefficient S making use of the frequency-domain LMS method with an error value defined as a difference of a product of the normalization coefficient S, the training vector X' and the windowed target impulse response B.sub.w to a product of the frequency-domain tap coefficient vector W.sub.w and the reception signal vector Y; PA1 a tap-coefficient update step of producing an updated tap coefficient vector W.sub.u by dividing a product of the windowed target response B.sub.w and the reception signal vector Y with the training vector X'; and PA1 a tap-coefficient windowing step of outputting the windowed tap coefficients w.sub.w (D) together with the normalization coefficient S, the windowed tap coefficients w.sub.w (D) being produced by transforming the updated tap coefficient vector W.sub.u into updated tap coefficients w.sub.u (D), selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients w.sub.u (D), normalizing the selected consecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients w.sub.w (D), and the normalization coefficient S being obtained by dividing the normalized consecutive coefficients with the selected consecutive coefficients before normalization.
However, the first and the fourth application wherein both the windowed target impulse response B.sub.w and the windowed tap coefficients w.sub.w (D) are updated with the same method do not always give stable convergence. Therefore, when the tap number L of the adaptive equalizer is larger than the duration v of the target impulse response, the second application is usually employed, and the third application is employed usually when the tap number L is smaller than the target duration v.
When the third application is employed, that is, when the windowed tap coefficients w.sub.w (D) is updated by the frequency-domain LMS method, however, following problems have been observed.
First, it takes certainly long time for the windowed target impulse response B.sub.w or the windowed tap coefficients w.sub.w (D) to converge. This is because the normalization, which is performed in the target-impulse-response windowing means 1400 for preventing the training from converging into B.sub.w =w.sub.w (D)=0, of the selected consecutive v taps of the time-domain target impulse response b.sub.u (D) affects the first term B.sub.w X' of the right side of equation (1) for giving the error value E to be used in equation (4) to calculate the updated tap coefficient vector W.sub.u, and makes the error value E at the tap-coefficient update means 1500 not equivalent to the error value E at the target-impulse-response update means 1300.
Second, the windowed target impulse response B.sub.w or the windowed tap coefficients w.sub.w (D) may rather diffuse than converge because of the same reason, when the noise signal n(D) of the transmission channel is comparatively large.